June 23, 1892] 



NATURE 



191 



meets the granite and basalt of that region ; a few miles eoiiih 

 the sandstone begins again and continues to Wady Haifa, 

 broken only by granite dykes. The granite is intrusive into an<l 

 alters the sandstone, whilst the latter reposes upon the basalt 

 and in some cases was deposited against upstanding basaltic 

 masses. Unmistakable lavas occur near the Nile east of 

 Minieh and west of Assiout. A description of some remarkable 

 f lults is given, and various minerals are noticed as occurring in 

 the sedimentary rocks and the bed of an ancient river. 



Mathematical Society, June 9.— Prof. Greenhill, F.R.S., 

 President, in the chair. — Prof. Henrici exhibited a model 

 of movable hyperboloids of one sheet. In 1873 he 

 gave a student at University College the problem to 

 construct a model of a hyperboloid of one sheet 

 by fixing three sticks anyhow, placing others so as to cut 

 these, and tying them together wherever they met. He told the 

 student that the system would soon become rigid, but was sur- 

 priseil to find that tiiis was not the case. It was easy to see the 

 reason of this fact, and thus he established the theorem : If the 

 two sets of generators of a hyperboloid be connected by articu- 

 lated joints wherever they meet, then the system remains movable, 

 the hyperboloid changing its shape. It was also soon found that 

 each point moves during this deformation along the normal to the 

 momentary position of the surface, and that therefore the different 

 positions of the surface constitute a system of confocal hyper- 

 boloids. He then made a model such that the generators 

 represented by sticks meet at points which lie on lines of cur- 

 vature of the hyperboloids. These describe, therefore, confocal 

 ellipsoids and hyperboloids of two sheets. In January 1874, 

 Prof. Henrici exhibited this model at a meeting of the Society. 

 Shortly afterwards a student made two copies of this model, and 

 these were fastened together in such a manner that both could 

 move together, remaining always confocal. It was this last 

 model that was now shown. The properties of the movable 

 hyperboloid became more widely known through a question 

 which Prof. Greenhill set in 1878 at the Mathematical Tripos 

 Examination, and this led Prof Cayley to give a solution of it 

 in the Messenger of Mathematics. Since that time several 

 French mathematicians have made further investigation of the 

 property in question. MM. Darboux and Mannheim, in par- 

 ticular, have made beautiful application of the deformable hyper- 

 boloid to the motion of a gyrating rigid body.— The following 

 further communications were made : — The second discriminant 

 of the ternary quantic, x'ti -f y'v + z'w, by Mr. J. E. Campbell. 

 If the ordinary discriminant of this quantic in x,y, z, be formed, 

 the result will be a quantic in x', y', z'. The discriminant of this 

 latter the writer believes vanishes identically with certain 

 exceptions. Prof. Henrici referred the author to a 

 paper by himself in vol. ii. of the Society's Proceedings. 

 — On the reflection and refraction of light from a magnetized 

 transparent medium, by A. B. Basset, F.R.S. The object 

 of this paper is to apply the theory of gyrostatically loaded media, 

 to investigate the reflection and refraction of light at the surface 

 of a magnetized transparent medium. This subject has been 

 partially discussed by Mr. Larmor in a paper communicated to 

 the Society last December, in which he has obtained the equa- 

 ! tions of motion of the medium ; but the paper in question contains 

 I (Mr. Basset thinks) a certain amount of vague and obscure 

 1 argument, founded upon general reasoning, which is calculated 

 to envelop the subject in a cloud of mystery, rather than to en- 

 lighten the understanding. He, therefore, finds it necessary 

 to write out the theory de novo, and to enter into a careful dis- 

 cussion respecting the boundary conditions. The principal 

 results are as follows : When the magnetic force is parallel to 

 the reflector, and also to the plane of incidence, the expressions 

 ; for the amplitudes of the reflected light are the same as those 

 i which he obtained by means of an extension of the electro- 

 magnetic theory (see Phil. Trans., 1891, p. 371) ; but when the 

 inagnetic force is perpendicular to the reflector, the above-men- 

 tioned expressions are of the same form as those furnished by 

 the electromagnetic theory, with the exception that the signs of 

 the magnetic terms are reversed. An experimental test of the 

 relative merits of the two theories might probably be obtained 

 by means of certain experiments performed by Prof. Kundt 

 (Berlin. Sitzungsberichte, July 10, 1884 ; translated Phil. Mag., 

 October 1884), but the mathematical work, although presentmg 

 no diflSculty, would be somewhat laborious. Having worked 

 out these results, he endeavours to obtain a theoretical explana- 

 tion of Kerr's experiments, on reflection from a magnet, by 

 combining the theory of gyrostatically loaded media with the 



NO. I 182, VOL. 46] 



theory of metallic reflection, explained in his book on " Physical 

 Optics," chapter xviii. sections 386-87; but the results are not 

 entirely satisfactory. This, however, is not surprising, inasmuch 

 as the theory of gyrostatically loaded media takes no account of 

 the statical effects of magnetization. — Note on approximate 

 evolution, by Prof. I.loyd Tanner. This note supplies a defi- 

 ciency in a paper (Math. Soc. Proc, vol. xviii.) in which Prof. 

 Hill pointed out the incorrectness of the rule for contracting the 

 processes of finding the square and cube roots of a number — 

 namely, it gives a practical test for determining the cases when 

 the rule can, and when it cannot, be safely applied.— A proof of 

 the exactness of Cayley 's number of seminvariants of a given 

 type, by Mr. E. B. Elliott, F.R.S.— Further note on auto- 

 morphic functions, by Prof. W. Burnside. 



Royal Meteorological Society, June 15.— Dr. C. 

 Theodore Williams, President, in the chair.— The following 

 papers were read : — English climatology, 1881-1890, by Mr. 

 F. C. Bayard. This is a discussion of the results of the climato- 

 logical observations made at the Society's stations, and printed 

 \xi\.\it Meteoi-ological Record {ox \.\\fi\.^x\ ^^■a.x?, 1881-1890. The 

 instruments at these stations have all been verified, and are ex- 

 posed under similar conditions, the thermometers being mounted 

 in a Stevenson screen, with their bulbs 4 feet above the ground. 

 The stations are regularly inspected, and the instruments 

 tested by the Assistant Secretary. The stations now 

 number about eighty, but there were only fifty-two which 

 had complete results for the ten years in question. The 

 author has discussed the results from these stations, and given 

 the monthly and yearly means of temperature, humidity, cloud, 

 and rainfall. His general conclusions are :— (l) With respect to 

 mean temperature, the sea coast stations are warm in winter and 

 cool in summer, whilst the inland stations are cold in winter and 

 hot in summer. (2) At all stations the maximum temperature 

 occurs in July or August, and the minimum in December or 

 January. (3) Relative humidity is lowest at the sea coast stations, 

 and highest at the inland ones. (4) The south-western district 

 seems the most cloudy in winter, spring, and autumn, and the 

 southern district the least cloudy in the summer months, and the 

 sea coast stations are, as a rule, less cloudy than the inland ones. 

 (5) Rainfall is smallest in April, and, as a rule, greatest in 

 November, and it increases from east to west. — The mean tem- 

 perature of the air on each day of the year at the Royal Obser- 

 vatory, Greenwich, on the average of the fifty years 1841 to 

 1890, by Mr. W. Ellis. The values given in this paper are 

 derived from eye observations from 1841 to 1848, and from the 

 photographic records from 1849 to 1890. The mean annual 

 temperature is 49°-5. The lowest winter temperature, 37°'2, 

 occurs on January 12, and the highest summer temperature, 

 63°-8, on July 15. The average temperature of the year is 

 reached in spring, on May 2, and in autumn on October 18. 

 The interval during which the temperature is above the average 

 is 169 days, the interval during which it is below the average 

 being 196 days. 



Sydney. 

 Royal Society of New South Wales, May 4.— Annual 

 Meeting.— H. C. Russell, F.R.S., President, in the chair.— 

 The report stated that 61 new members had been elected 

 during the year, and the total number on the roll on April 30 

 was 478. During the year the Society held eight meetings, at 

 which the following papers were read :— Presidential addfe.ss, by 

 Dr. A. Leibius. — Notes on the large death-rate among 

 Australian sheep in country infected with Cumberland disease 

 or splenic fever, and Notes on a spontaneous disease among 

 Australian rabbits, by Adrien Loir. — Compressed-air flying 

 machines, Nos. 13 and 14, and on a wave-propelled vessel, by 

 L. Hargrave. — A cyclonic storm or tornado in the Gwydir 

 district ; Preparations now being made in Sydney Observatory 

 for the photographic chart of the heavens ; Notes on some 

 celestial photographs recently taken at Sydney Observatory ; and 

 Notes on the rate of growth of some Australian trees, by H. C. 

 Russell, F. K.S.— Some folk-songs and myths from Samoa, 

 translated by the Rev. G. Pratt, with introductions and notes, 

 by Dr. John Eraser. — Notes on the use, construciion, and cost 

 of service reservoirs, by C. W. Darley. — On the constitution of 

 the sugar series, by W. M. Hamlet.— On kaolinite from the 

 Hawkesbury Sandstone, by H. G. Smith. — A contriijuiion to 

 the microscopic structure of some Australian rocks, by the Rev. 

 J. Milne Curran. — On some New South Wales and other 

 minerals (note No. 6), by Prof. Liversidge, F.R.S. —Artesian 



